Medial axis transformation as a solid modeling representation method for computer aided design software

Abstract

A method for achieving a representation of an object within a data structure for a Computer Aided Design system employing a Medial Axis Transformation (MAT), the representation of the object comprising a set of adjacent bounded surface elements called MAT faces, the MAT faces being bound by sets of MAT edges, which are portions of curves lying on a surface of the MAT faces on either side of the edge, and points where several MAT faces meet are called MAT vertices. The method comprises at least defining each of the MAT vertices as points in a space domain; assigning a radius function to each of the MAT vertices, based on only a single value; defining each of the MAT edges as a curve in space; defining limits of each of the MAT edges as two MAT vertexes which lie on the curve; assigning a radius function to each of the MAT edges; defining each of MAT faces as a surface in space; defining the limits of each of the MAT faces as a MAT loop, comprising at least three MAT edges, sharing each a MAT node, whereby a direction, clockwise or counter-clockwise, of the MAT loop defines on which side of the MAT loop the MAT face will be formed; defining the MAT links as the edges which are shared by at least two MAT faces; assigning a radius function to each of the MAT faces; and defining a MAT object as a connected set of MAT faces, edges and vertices.

1 . A method for achieving a representation of an object within a data structure for a Computer Aided Design (CAD) system employing a Medial Axis Transformation (MAT), the representation of the object comprising a set of adjacent bounded surface elements called medial axis transformation faces, the medial axis transformation faces being bound by sets of medial axis transformation edges, which are portions of curves lying on a surface of the medial axis transformation faces on either side of the edge, and points where several medial axis transformation faces meet are called medial axis transformation vertices, the method comprising at least
 defining each of the medial axis transformation vertices as points in a space domain;   assigning a radius function to each of the medial axis transformation vertices, based on only a single value;   defining each of the medial axis transformation edges as a curve in space;   defining limits of each of the medial axis transformation edges as two medial axis transformation vertexes which lie on the curve;   assigning a radius function to each of the medial axis transformation edges;   defining each of medial axis transformation faces as a surface in space;   defining the limits of each of the medial axis transformation faces as a medial axis transformation loop, comprising at least three medial axis transformation edges, sharing each a medial axis transformation node, whereby a direction, clockwise or counter-clockwise, of the medial axis transformation loop defines on which side of the medial axis transformation loop the medial axis transformation face will be formed;   defining the medial axis transformation links as the edges which are shared by at least two medial axis transformation faces;   assigning a radius function to each of the medial axis transformation faces; and   defining a medial axis transformation object as a connected set of medial axis transformation faces, edges and vertices.   
     
     
         2 . The method of  claim 1 , where in the step of assigning the radius function to each of the medial axis transformation edges, the function is linear, whereby the radius varies linearly along the medial axis transformation edge. 
     
     
         3 . The method of  claim 1 , where in the step of assigning the radius function to each of the medial axis transformation edges, the function is non-linear, whereby the radius does not vary linearly along the medial axis transformation edge. 
     
     
         4 . The method of  claim 1 , where in the step of assigning the radius function to each of the medial axis transformation edges, the function is defined numerically, piece-wise linear or by other methods to define numerical functions. 
     
     
         5 . The method of  claim 1 , where in the step of assigning the radius function to each of the medial axis transformation faces, the function is linear, whereby the medial axis transformation vertices and medial axis transformation edges are linear and coplanar. 
     
     
         6 . The method of  claim 1 , where in the step of assigning the radius function to each of the medial axis transformation faces, the function is non-linear. 
     
     
         7 . The method of  claim 1 , where in the step of assigning the radius function to each of the medial axis transformation edges, the function is defined numerically, piece-wise linear or other methods for defining numerical functions. 
     
     
         8 . The method of  claim 1 , wherein the representation of the object is achieved together with a Boundary Representation (BREP), further comprising
 for each medial axis transformation data structure element, assigning a link to boundary representation data structure elements defining the respective medial axis transformation element; and   for each boundary representation data structure element assign a link to the medial axis transformation data structure elements defining the respective boundary representation element.   
     
     
         9 . A Computer Aided Design CAD system configured to implement geometric engine functions that use a medial axis transformation based data structure as a solid representation method. 
     
     
         10 . The system of  claim 9 , wherein the geometric engine functions use the medial axis transformation based data structure solid representation method together with a boundary representation method. 
     
     
         11 . A Computer Aided Design CAD system configured to implement part and assembly modeling functions that use a medial axis transformation based data structure as a solid representation method. 
     
     
         12 . The system of  claim 11 , wherein the part and assembly modeling functions use the medial axis transformation based data structure solid representation method together with a boundary representation method. 
     
     
         13 . A user interface configured to enable a creation and manipulation of objects represented by a medial axis transformation-based data structure at least as a solid representation method. 
     
     
         14 . The method for achieving a representation of an object within a data structure for a Computer Aided Design (CAD) system of  claim 1 , wherein the representation of the object further comprises a 4th parameter corresponding to time and a medial axis transformation shell, thereby enabling a 4-dimensional solid representation method. 
     
     
         15 . A Computer Aided Design CAD system configured to implement geometric engine functions that use a 4-dimensional solid representation method. 
     
     
         16 . A Computer Aided Design CAD system configured to implement part and assembly modeling functions that use a 4-dimensional solid representation method. 
     
     
         17 . A user interface configured to enable a creation and manipulation of objects represented in a 4-dimensional environment by a 4-dimensional solid representation method.